Demarcating system

ABSTRACT

A demarcating system for indicating the boundary of an area to an object (for example a robot, such as a robotic lawnmower), which has a receiver for receiving electromagnetic signals. The system includes a control system, a wire loop, a signal generator, and current sensing circuitry. The wire loop can be arranged by a user along a path, so as to indicate the path to the object as part of a boundary of the area. The signal generator is electrically connected to the wire loop in order to apply voltage signals thereto, such signals causing the emission of corresponding electromagnetic boundary indicating signals from the wire loop that may be received by the receiver of the object. The signal generator is under the control of the control system with the voltage signals applied by the signal generator to the wire loop being controlled by the control system. The current sensing circuitry senses current signals present within the wire loop and the processors of the control system analyse such current signals. The processors of the control system are programmed to operate in a calibration mode whereby they: cause the signal generator to apply a series of test voltage waveforms to the wire loop, each of the test voltage waveforms generating a corresponding current waveform within the wire loop; and analyse the series of corresponding current waveforms, as sensed by the current sensing circuitry, so as to determine an operating voltage waveform that, when applied to the wire loop, generates a corresponding operating current waveform that is substantially the same shape as a predetermined current waveform.

TECHNICAL FIELD

The present invention relates to demarcating systems and, in particularto demarcating systems for indicating the boundary of an area to anobject, such as an electronic device (and in particular a robot), avehicle, or a person or animal (e.g. a pet).

BACKGROUND

Certain demarcating systems may indicate the boundary of an area to anobject using a wire loop, through which a current is passed, thusgenerating an electromagnetic signal that may be received by a receiverassociated with the object. The wire loop may be arranged along a path(typically, though not necessarily, a closed path), with this path beingindicated to the object as part of, or the entire boundary of the area.

In some cases, the system may allow the user to adjust the length andshape of the wire loop, for example so as to be suitable for demarcatingthe boundary of a particular area. The Applicant has recognised thatthis may pose challenges to the reliability of the system, since thesignal received by the receiver associated with the object may vary as aresult of changes in the length and shape of the wire loop.

SUMMARY

Aspects of the invention are set out in the appended claims.

The following disclosure describes a demarcating system for indicatingthe boundary of an area to an object, the object having a receiver forreceiving electromagnetic signals. The system comprises: a controlsystem comprising one or more processors; a wire loop, which may bearranged by a user along a path, so that said path is indicated to theobject as at least part of the boundary of the area, the length of thewire loop being adjustable by the user; a signal generator, which iselectrically connected to the wire loop so as to be operable to applyvoltage signals thereto, which cause the emission of correspondingelectromagnetic boundary indicating signals from the wire loop forreceipt by the receiver of the object, the signal generator being underthe control of the control system such that the voltage signals appliedby the signal generator to the wire loop are controlled by the controlsystem; current sensing circuitry, which is electrically connected tothe wire loop so as to sense current signals present within the wireloop and which is connected to the control system so that its processorscan analyse current signals present within the wire loop.

The one or more processors are programmed to operate in a calibrationmode whereby they: cause the signal generator to apply a series of testvoltage waveforms to the wire loop, each of the test voltage waveformsgenerating a corresponding current waveform within the wire loop; andanalyse the series of corresponding current waveforms, as sensed by thecurrent sensing circuitry, so as to determine an operating voltagewaveform that, when applied to the wire loop, generates a correspondingoperating current waveform that, when normalized, is substantially thesame as a predetermined current waveform.

In some embodiments, the voltage and current waveforms may be periodicwaveforms, for example consisting of a cycle that is repeatedcontinuously (e.g. sine waves, square waves, triangular waves, sawtoothwaves, and the like). In addition, or instead, the voltage and currentwaveforms may be bipolar, having significant positive and negativeportions. Additionally, or alternatively, they may be polarityasymmetric, so that the negative portions are differently shaped to thepositive portions.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will now be described with reference to the drawings, inwhich:

FIG. 1 is schematic diagram of a demarcating system according to anexample embodiment of the present invention;

FIG. 2A is a graph showing an example of a desired current waveform fora wire loop;

FIG. 2B is a graph showing a distorted version of the current waveformof FIG. 2A;

FIG. 2C is a graph showing a further distorted version of the currentwaveform of FIG. 2A; and

FIG. 3 is a circuit diagram representing an approximation of thedemarcating system shown in FIG. 1.

DETAILED DESCRIPTION OF THE DRAWINGS

Turning first to FIG. 1, there is shown a schematic diagram of ademarcating system 1 according to an example embodiment of the presentinvention.

The demarcating system 1, when activated, indicates to an object 50 theboundary 20 of an area 30. The object may be an electronic device, andin particular a robot, such as a robotic lawnmower; a vehicle; or aperson or animal (e.g. a pet).

As may be seen from the drawing, the demarcating system includes a wireloop 20, a signal generator 12, current sensing circuitry 14, and acontrol system 15.

As illustrated in the drawing, the wire loop 20 has been arranged by auser along a path. As a result, the path of the wire loop 20 isindicated to the object 50 as the boundary of the area (or a partthereof). Where the object 50 is a robotic lawnmower, the wire loop 20may, for example, indicate to the robot the path of at least part of aboundary of an area to be mowed.

The length and shape of the wire loop 20 may be adjusted by the user,for example so as to be suitable for a particular area of interest. Forinstance, as shown in FIG. 1, the user may cut the wire to a desiredsize and then connect it to connectors 18 a, 18 b, thereby electricallyconnecting the wire loop 20 to the signal generator 12 and the currentsensing circuitry 14. It will of course be appreciated that this ismerely one example of how the wire loop 20 may be electrically connectedto the signal generator 12 and current sensing circuitry 14 and that awide variety of other arrangements to provide such electrical connectionare possible.

When the system is activated, the signal generator 12 applies voltagesignals to the wire loop 20, with these voltage signals causing theemission of corresponding electromagnetic boundary indicating signalsfrom the wire loop 20 that may then be received by a receiver 101associated with the object 50. Specifically, the voltage signalsgenerate corresponding current signals in the wire loop 20, with thesecurrent signals in turn produce a time-varying magnetic field in thevicinity of the wire loop 20—and in particular the in the area 30—aswell as an associated time-varying electric field; thus, electromagneticboundary indicating signals are emitted by the wire loop 20.

As shown in FIG. 1, the receiver 101 may form a part of a receivingsystem 100 associated with the object 50. As also shown in FIG. 1, thisreceiving system 100 may further include one or more processors 102 thatare connected to the receiver so that they can analyse theelectromagnetic signals received by the receiver 101.

The receiver 101 of the receiving system 100 may, for example, beconfigured to sense the (time-varying) magnetic field component of theelectromagnetic boundary indicating signals that are emitted by the wireloop 20: the magnetic field component will typically be more easilysensed than the electric field component, given the respective shapes ofthe magnetic and electric fields within the area 30. In order to sensethe magnetic field component (or otherwise), the receiver may includeone or more conductive coils.

As indicated in FIG. 1 by the dashed line linking the signal generator12 and the control system 15, the signal generator is under the controlof the control system 15, which, as may also be seen from FIG. 1,includes at least one processor 16. As a result, the voltage signalsapplied by the signal generator 12 to the wire loop 20 are controlled bythe control system 15. For instance, the signal generator 12 and thecontrol system 15 may have an electrical or wireless connection thatallows control signals to be sent to the signal generator 12, with thesecontrol signals specifying the voltage signals that the signal generator12 should apply to the wire loop 20.

The electrical connection of the current sensing circuitry 14 to thewire loop 20 enables the current sensing circuitry 14 to sense currentsignals present within the wire loop 20. Where the receiver 101 of thereceiving system 100 is configured to sense the (time-varying) magneticfield component of the electromagnetic boundary indicating signalsemitted by the wire loop 20, the current signals present within the wireloop 20 may be of particular importance, since these will directlydetermine the magnetic field component of the electromagnetic boundaryindicating signals.

The current sensing circuitry 14 may, for example, be electricallyconnected in series with the wire loop 20, as illustrated in FIG. 1. Asindicated by the dashed line in FIG. 1 linking the current circuitry 14to the control system 15, the current circuitry 14 is connected to thecontrol system 15 so that the processor(s) 16 of the control system 15can analyse current signals present within the wire loop 20.

In one example, the current sensing circuitry 14 may include a resistorhaving a known resistance (which resistor may be designed so that thisvalue is insignificant in comparison to other sources of resistancewithin the circuit that includes the wire loop 20), with a lead fromeach end of the resistor being connected to a respective input to theprocessor(s) 16. Hence (or otherwise), the processor(s) 16 may determinethe potential difference across the resistor and, using the knownresistance value, the current present within the wire loop 20. In thisexample, the processor(s) 16 may be viewed as providing part of thecurrent sensing circuitry 14; this may also be the case in otherexamples of current sensing circuitry 14.

In another example, the current sensing circuitry 14 may include aresistor having a known resistance (which resistor may again be designedso that this value is insignificant in comparison to other sources ofresistance within the circuit that includes the wire loop 20), and avoltage sensor electrically connected to the resistor so as to sense thevoltage across it. This voltage sensor may then be connected to thecontrol system 15 (for example by an electrical or wireless connection)such that it can send data to the control system 15 concerning thevoltage across the resistor, and, because the value of its resistance isknown, thus the current signals present in the wire loop. In suchexamples of current sensing circuitry an analogue-to-digital convertermay optionally be included that converts the analogue voltage signalinto a digital signal for processing by the processor(s) 16. In otherexamples, analogue-to-digital converters may likewise be included so asto, for example, convert analogue current or voltage signals intocorresponding digital signals for processing by the processor(s) 16.

In a still further example, the current sensing circuitry 14 may includea Hall effect current sensor. Such current sensing circuitry 14 maysuitably introduce negligible additional resistance to the circuitincluding the wire loop 20. The output from this Hall effect currentsensor may, for example, be provided directly to the processor(s) 16,or, in another example, be passed to an analogue-to-digital converter,which then provides an output to the processor(s) 16.

In the particular example illustrated in FIG. 1, the signal generator12, current sensing circuitry 14, and the control system 15 are allprovided within a base station 10. As also shown in FIG. 1, theconnectors 18 a, 18 b for electrically connecting the wire loop 20 tothe signal generator 12 and current sensing circuitry 14 may be providedon the exterior of the base station.

In examples where the object 50 is a robot (and potentially in otherexamples), this base station 10 may optionally function as a chargingstation, to which the robot (or, more generally, the object 50) returnsperiodically to recharge its internal power source using power providedby the charging station.

The processor(s) 16 of the control system 15 may be programmed tooperate in a number of modes. In each of these modes the control system15 may command components of the demarcating system that are under itscontrol (such as the signal generator 12) to operate in accordance withrules and procedures that are associated with the mode selected by theuser.

Calibration Mode

In particular, it is envisaged that the processor(s) 16 are programmedto operate in a calibration mode. This may, for example, be utilised toadjust the voltage signals generated by the signal generator 12 in sucha way that the electromagnetic signals produced by the wire loop 20 andreceived at a point within area 30 have a desired shape (when consideredwith respect to time). In other words, the electromagnetic signalsproduced by the wire loop 20 and received at a point within area 30,when normalized, are substantially the same as a desired electromagneticsignal.

With a number of types of receiving systems 100, in order for theelectromagnetic signal received by the receiver 101 to be correctlyanalysed by the receiving system 100 (e.g. by the processor(s) 102), itmay be important that the electromagnetic signal has a specific shapewhen considered with respect to time. For example, where the receiver101 of the receiving system 100 is configured to sense the time-varyingmagnetic field component of the electromagnetic boundary indicatingsignals emitted by the wire loop 20, it may be important that themagnetic field component has a specific shape.

However, changes made by the user to the length and/or shape of the wireloop are likely to affect the shape of the electromagnetic signalproduced by the wire loop. For instance, changes to the length of thewire loop 20 will tend to alter the resistance and impedance of the wireloop: increasing the length of the wire loop 20 will tend to increaseboth its impedance and resistance, whereas decreasing the length of thewire loop 20 will tend to decrease both its impedance and resistance.Further, changes to the shape of the wire loop 20 may alter itsimpedance, even if its length remains the same.

It should be noted that, it may be of lesser importance what thisspecific signal shape is (a variety of signal shapes may be appropriate,for instance amplitude modulation, frequency modulation, pulses etc. maybe utilised) than it is that the signal shape is substantially the sameregardless of how the user has set up the loop, for example in terms ofits length and shape.

Nonetheless, solely for the purposes of illustration, attention isdirected to FIG. 2A, which is a graph showing an example of a suitablecurrent waveform that it is desired to apply to the wire loop 20;current is shown on the ordinate and time on the abscissa. As may beseen, the waveform 200A consists of a cycle that is repeatedcontinuously with period T (indicated in the drawing by a double-headedarrow). The specific example shown is a combination of a sine wave witha cosine wave having double the frequency.

It may be noted that the waveform 200A is polarity asymmetric; thus, thenegative portions are differently shaped to the positive portions. Inaddition, the waveform 200A is bipolar, having significant positive andnegative portions. Waveforms that are bipolar and polarity asymmetricmay be useful in enabling the receiving system 100 to determine whetherthe object 50 is inside or outside of the area 30, as the signalreceived by the object's receiver 101 will typically differsubstantially depending on whether it is inside or outside of the area30.

Furthermore, it may be noted that in the particular example shown, acomplete cycle of the current waveform has a different number ofpositive 211, 212 and negative 221 peaks. Specifically, a complete cyclehas two positive peaks 211, 212 and only one negative peak 221. Having adifferent number of positive and negative peaks may assist theprocessor(s) 102 of the receiving system 100 in determining whether theobject 50 is inside or outside of the area. For example, theprocessor(s) 102 of the receiving system 100 may count the number ofpositive and/or negative peaks during a given time interval, or they maydetermine the number of times the signal exceeds a certain threshold.

Turning now to FIG. 2B, shown is a graph showing a distorted version200B of the current waveform 200A of FIG. 2A. The same operating voltagewaveform as in FIG. 2A is provided by the signal generator 12, but theuser has set up the wire loop differently 20, resulting in a change tothe impedance and resistance of the wire loop 20 and a correspondingdistortion of the current waveform 200B, as compared with that of FIG.2A. Specifically, the cosine component has been phase-shifted.

Nonetheless, despite the distortions of the current waveform 200B, eachcomplete cycle still includes two positive peaks 211, 212 and onenegative peak 221. Thus, the receiving system 100 may still successfullydetermine whether the object 50 is inside or outside of the area 30.

FIG. 2C is a graph showing a further distorted version 200C of thecurrent waveform 200A of FIG. 2A. The same operating voltage waveform asin FIG. 2A and FIG. 2B is provided by the signal generator 12, but theuser's set up of the wire loop 20 has resulted in still greaterdistortion of the current waveform 200C. As may be seen, the currentwaveform is sufficiently distorted that each complete cycle includes twopositive peaks 211, 212 and two negative peaks 221, 222. As a result, itmay be problematic for the receiving system 100 to determine whether theobject 50 is inside or outside of the area 30.

The calibration mode may enable the demarcating system to diminishdistortions of the current waveform, such as those illustrated in FIGS.2A-2C, that are caused by the particular user setup of the wire loop 20(it being recognised that the current waveforms 200A-C and the way inwhich the receiving system 100 of the object 50 operates are merelyillustrative and that a wide range of waveforms are suitable for usewith demarcating systems as described herein).

Accordingly, in the calibration mode, the processor(s) 16 of the controlsystem 15 determine(s) an operating voltage waveform that, when appliedto the wire loop 20, may be expected to generate an operating currentwaveform having the same shape as a predetermined current waveform. Whenthis predetermined current waveform is present within the wire loop 20,the wire loop 20 emits electromagnetic signals having a desired shapewith respect to time. In particular, it should be understood that theshape of the time-varying magnetic component of such electromagneticsignals will closely correspond to the shape of the current signalspresent within the wire loop 20.

This predetermined current waveform will typically be predefined in thedemarcating system prior to delivery to the user, though in some casesthe system could enable the user to define the current waveform. Forinstance, the predetermined current waveform may be pre-programmed inthe processor(s) 16 or the signal generator 12, or stored on datastorage forming part of the control system 15 or another part of thedemarcating system 1.

In order to determine such an operating voltage waveform, the controlsystem 15 (specifically, the processor(s) 16 thereof) causes the signalgenerator 12 to apply a series of test voltage waveforms to the wireloop 20. Each of these test voltage waveforms generates a correspondingcurrent waveform within the wire loop 20. The current sensing circuitry14, as a result of its electrical connection to the wire loop 20, isable to sense the series of corresponding current waveforms. Theprocessor(s) 16 of the control system 15 are, in turn, able to analysethem, as a result of the connection between the control system 15 andthe current sensing circuitry 14. By analysing the series of currentwaveforms, the processor(s) 16 are able to determine an operatingvoltage waveform that results in the generation within the wire loop 20of an operating current waveform with the desired shape and, inconsequence, the emission from the wire loop 20 of electromagneticsignals of the desired shape.

It will be noted that the operation of the demarcating system 1 in sucha calibration mode does not require the involvement of the receiver 101(or, more generally, the receiving system 100). A possible consequenceis that the calibration may be more accurate, since communication overthe—not yet calibrated—channel provided by the wire loop 20 and thereceiver 101 does not need to be utilised.

In some cases, in the calibration mode the processor(s) 16 may determinean operating voltage waveform that results in an operating currentwaveform with not only the same shape as a predetermined currentwaveform, but also the same magnitude. Thus, in such cases, theoperating current waveform is substantially the same as thepredetermined current waveform. This might, for example, be of benefitwhere the receiving system 100 utilises the strength of theelectromagnetic signal received by its receiver 101 (e.g. the strengthof the magnetic field component) to determine an estimate of itsdistance (and therefore the distance of the object 50) from theboundary. More generally, this might be utilised to ensure that theelectromagnetic signals emitted by the wire loop 20 have sufficientstrength to be reliably received at some predefined, or user-defined,distance from the wire loop 20.

In some cases, each of the series of test voltage waveforms utilised inthe calibration mode may be substantially sinusoidal. This may in somecases simplify the analysis of the corresponding series of currentsignals by the processor(s) 16, since the response of circuits tosinusoidal signals is generally more straightforward to represent usingalgebraic expressions.

Furthermore, where the circuit can be assumed to behave approximatelylinearly (which assumption will be valid in a number of cases) theeffects of such sinusoidal test voltage waveforms may be assumed to sumlinearly. In addition, the application of a sinusoidal voltage waveformmay be assumed to result in a sinusoidal current waveform of the samefrequency. A possible consequence is that the determination of asuitable operating voltage waveform (one that when applied to the wireloop 20 generates a corresponding operating current waveform of desiredshape), may become more straightforward.

More particularly, where the test waveforms utilised in the calibrationmode are substantially sinusoidal, the processor(s) 16 may, for example,be programmed to carry out a frequency domain linear transformation ofthe predetermined current waveform (whose shape we are seeking tomatch). For instance, the linear transformation may be a Fouriertransform or a Laplace transform.

Such a frequency domain linear transformation (e.g. a Fourier transform)may allow the predetermined current waveform I(t) to be represented asthe superposition of n sinusoidal current waveforms, each of which has arespective frequency f_(k), phase shift θ_(k), and weighting coefficientor amplitude value B_(k) (with the index k identifying the sinusoidalwaveform in question). Thus:

${I(t)} = {\sum\limits_{k = 1}^{n}{B_{k}{\sin ( {{2\pi \; f_{k}t} + \theta_{k}} )}}}$

It should be understood however that such a representation of thepredetermined current is by no means reliant upon the use of a frequencydomain linear transformation. For instance, the parameter values of thesinusoidal current waveforms (f_(k), θ_(k) and B_(k)) may simply bepredefined or pre-programmed in the demarcating system (this being anexample of the predetermined current waveform being pre-programmed intothe demarcating system prior to delivery to the user). For example,these values may be pre-programmed in the processor(s) 16 or the signalgenerator 12, or stored on data storage forming part of the controlsystem 15 or another part of the demarcating system 1.

Where the predetermined current waveform 40 can be represented as thesuperposition of n sinusoidal current waveforms, the operating voltagewaveform may, in some cases, similarly be represented as thesuperposition of n sinusoidal voltage waveforms. It will be understoodthat n will be at least 2 and, where a frequency domain lineartransformation has been carried out, may be large, e.g. more than 100;however, particularly where the sinusoidal current waveforms arepredefined or pre-programmed n may conveniently be less than or equal to10 (and in some cases may be less than or equal to 5), so as to simplifythe calculations.

More particularly, each of these n sinusoidal voltage waveforms may havea respective phase shift ψ_(k), and amplitude value A_(k), as well ashaving the same frequency f_(k) as a respective one of the n sinusoidalcurrent waveforms. Thus:

${V(t)} = {\sum\limits_{k = 1}^{n}{A_{k}{\sin ( {{2\pi \; f_{k}t} + \psi_{k}} )}}}$

In such cases, the determination of a suitable operating voltagewaveform may, for example, involve the processor(s) 16 analysing theseries of current waveforms that result from the series of test voltagewaveforms so as to determine suitable parameter values (e.g. phase shiftand amplitude values ψ_(k), A_(k)) for the sinusoidal voltage waveformsof the operating voltage waveform. A number of approaches may beemployed to determine these parameter values. Below there are describedtwo detailed examples of suitable approaches.

First Example Approach

In the first example approach, each of the test voltage waveforms issinusoidal and has the same frequency, f_(k), as a respective one of then sinusoidal current waveforms. Thus, the kth test voltage waveform,v_(k)(t), is given by:

v _(k)(t)=α_(k) sin(2πf _(k) t)

When such a test voltage waveform is applied to the wire loop, it may beexpected that the resulting current signal will be given by:

${i_{k}(t)} = {\frac{a_{k}}{Z_{k}}{\sin ( {{2\pi \; f_{k}t} + \Phi_{k}} )}}$

Where Z_(k) is an impedance value and Φ_(k) is a phase shift value forthe frequency in question. It should be appreciated that such values maybe determined empirically by analysing the series of current waveformsi_(k)(t). For example, Φ_(k) may be determined by calculating the phasedifference between v_(k)(t) and i_(k)(t), whereas Z_(k) may bedetermined by calculating the ratio between the peak voltage value andthe peak current value (or the ratio between the RMS values, thepeak-to-peak values etc.).

The thus-determined impedance and phase shift values Z_(k), Φ_(k) maythen be used to determine suitable parameter values (e.g. phase shiftand amplitude values ψ_(k), A_(k)) for the sinusoidal voltage waveformsof the operating voltage waveform V(t).

For example, if we know that the kth test voltage waveform results in aphase shift of Φ_(k) and we are seeking a suitable phase shift ψ_(k) forthe kth sinusoidal voltage waveform of the operating voltage waveformV(t) such that the corresponding kth sinusoidal current waveform willhave a phase shift value of θ_(k), then the phase shift produced by thekth test voltage waveform, Φ_(k), may simply be subtracted from thedesired phase shift value, θ_(k). Thus:

ψ_(k)=θ_(k)−Φ_(k)

Similarly, if we know that the kth test voltage waveform results in acurrent of amplitude a_(k)/Z_(k) and we are seeking a suitable voltageamplitude value A_(k) for the kth sinusoidal voltage waveform of theoperating voltage waveform V(t) such that the corresponding kthsinusoidal current waveform will have an amplitude of B_(k), then A_(k)should be equal to B_(k) multiplied by the impedance value Z_(k). Thus:

A_(k)=Z_(k)B_(k)

Accordingly, the operating voltage waveform V(t) may be expressed as:

${V(t)} = {\sum\limits_{k = 1}^{n}{Z_{k}B_{k}{\sin ( {{2\pi \; f_{k}t} + \theta_{k} - \Phi_{k}} )}}}$

It should be noted that the number m of test voltage waveforms v_(k)(t)may be different to, for example less than, the number n of sinusoidalvoltage waveforms of the operating voltage waveform V(t) (also thenumber of sinusoidal current waveforms of the predetermined currentwaveform I(t)).

Thus, where m <n there will (generally speaking) be certain frequenciesf_(k) for which there is no associated test waveform and, therefore, noassociated impedance and phase shift values Z_(k), Φ_(k) that have beendetermined empirically. Hence, (or otherwise) suitable impedance andphase shift values Z_(k), (1)_(k) for those frequencies may bedetermined, for example by analysing the impedance and phase shiftvalues Z_(k), Φ_(k) for other frequencies, e.g. by interpolation and/orextrapolation of the empirically-determined values. Such an approach maybe particularly appropriate where n is large.

Second Example Approach

In the second example approach, the test voltage waveforms sweep over afrequency range from f _(min) to f_(max) in order to identify a resonantfrequency within this range. Accordingly, each of the series of testvoltage waveforms has substantially the same shape, but a differentrespective frequency.

The resonant frequency will, in many cases, depend on the respectivevalues for the sources of inductance, capacitance and resistance withinthe same circuit as the wire loop 20. In some cases, for example withsinusoidal waveforms, this relationship may be described by a relativelysimple algebraic relation (as will be discussed below). Nonetheless, inother cases, it may still be possible to find at least an empiricalrelationship based on these values (or perhaps a more complex algebraicrelation).

A value for the capacitance of the circuit may be known, for example bytesting prior to shipping to the customer, since variations in the wireloop typically will not alter the capacitance of the circuit.

A value for the resistance in the circuit may be determined empirically,for example by calculating, measuring or otherwise determining theimpedance at the resonant frequency, Z(f₀). It should be noted howeverthat the value of R might also be determined by other means, for exampleapplying a DC voltage signal to the circuit and measuring the impedance,which may be substantially equal to the resistance.

In some embodiments, therefore, the processor(s) 16 of the controlsystem 15 may determine the operating voltage waveform using suchvalues. For instance, using a formula or look-up table based on suchvalues.

In a specific implementation of the second example approach, the testvoltage waveforms are sinusoidal. (which are again sinusoidal) sweepover a frequency range from f_(min) to f_(max). Thus, each of the testvoltage waveforms is sinusoidal and has a respective frequency, with thefrequencies of the series of test voltage waveforms being distributedover this frequency range. For instance, frequencies may substantiallyequally distributed over the frequency range, with consecutivefrequencies differing by a substantially constant amount.

According to the second approach, the current waveforms corresponding tothe test waveforms are analysed so as to identify the resonant frequencyf₀ for the demarcating system. A sinusoidal voltage waveform having thisfrequency will produce a current waveform having the maximum amplitude(as compared with sinusoidal voltage waveforms having other frequencieswithin the test range).

It should be noted that the system may not actually generate a testvoltage waveform having exactly the resonant frequency f₀. Rather,interpolation may be used to identify the frequency f₀ at which theamplitude of the current waveform is expected to be at a maximum.

A number of sweeps of the frequency range (or portions thereof) may becarried out. For instance, a first sweep might start at an end-point ofthe frequency range (either f_(min) or f_(max)), with a succession oftest voltage waveforms being applied whose frequencies are spaced apartby a first amount. Once a turning point has been reliably detected, forinstance where the current amplitude has been steadily increasing witheach consecutive test voltage waveform and then decreases steadily for anumber of consecutive test voltage waveforms, a second sweep over asmaller portion of the frequency range may be carried out, with asuccession of test voltage waveforms being applied whose frequencies arespaced apart by a second, smaller amount. Again, this may continue untila turning point has been reliably detected, whereupon a further sweepmay be carried out, or a value for the resonant frequency f₀ may becalculated by interpolating the available data.

Thus, a plurality of sweeps of portions of the frequency range may becarried out, for example with each portion being narrower than theprevious portion. In addition (or instead), the spacing of frequencieswithin each sweep may be smaller than that in the previous sweep.

It should be noted that the end-point values of the frequency range,f_(min) and f_(max) may be predetermined, for example based on thelikely minimum and maximum lengths for the wire loop 20.

Once a value for the resonant frequency f₀ has been calculated, this maybe utilised to determine a suitable operating voltage waveform (one thatwhen applied to the wire loop 20 generates a corresponding operatingcurrent waveform of desired shape). It should be appreciated that, inmany cases, the resonant frequency f₀ will be related to the respectivevalues for the sources of inductance, capacitance and resistance withinthe same circuit as the wire loop 20 according to an algebraic relation.

Further, the impedance for a sinusoidal voltage waveform having aparticular frequency Z(f) will also, in many cases, be related to therespective values for the sources of inductance, capacitance andresistance within the same circuit as the wire loop 20 according to analgebraic relation. Similarly, the phase difference Φ(f) between asinusoidal voltage waveform and its corresponding sinusoidal currentwaveform will also, in many cases, be related to the respective valuesfor the sources of inductance, capacitance and resistance within thesame circuit as the wire loop 20 according to an algebraic relation.

Accordingly, in a number of cases it is possible to derive an algebraicexpression for each of the impedance Z(f) and the phase difference Φ(f)at frequency f, in terms of the frequency in question f, the resonantfrequency f₀, and one or more known values corresponding to the othersources of resistance and/or capacitance within the same circuit as thewire loop 20. Hence (or otherwise), it may be possible to determinesuitable parameter values (e.g. phase shift and amplitude values ψ_(k),A_(k)) for the sinusoidal voltage waveforms of the operating voltagewaveform using such known values and the calculated value of theresonant frequency f₀.

A specific example of this will now be described with reference to FIG.3, which is a circuit diagram representing an approximation of thedemarcating system shown in FIG. 1. According to the approximation shownin the diagram, the components other than the wire loop 20, such as thesignal generator 12, the current sensing circuitry 14 and the controlsystem 15 may be represented as a combination of a resistor (withresistance R₁), a capacitor (with capacitance C) and a voltage source(having a time-varying voltage V) connected in series. As discussedabove, the signal generator 12, the current sensing circuitry 14 and thecontrol system 15 may be provided within a base station 10, which isindicated in the drawing using dashed lines. Further, according to theapproximation shown in FIG. 3, the wire loop 20 may be represented as acombination of a resistor (with resistance R₂) and inductor (withinductance L).

This approximation will be valid in a number of cases since the wireloop 20 will often be the dominant source of inductance within thecircuit and, by contrast, the wire loop 20 will often provide negligiblecapacitance in comparison with other components within the same circuit,such as the signal generator 12, current sensing circuitry 14 etc.

For such a circuit, the impedance Z(f) at frequency f, is given by:

$\begin{matrix}{{Z(f)} = \sqrt{R^{2} + ( {\frac{1}{2\pi \; {fC}} - {2\pi \; f\; L}} )^{2}}} & (1)\end{matrix}$

Where R is the total resistance, and thus: R=R₁+R₂.

The phase difference Φ(f) between (sinusoidal) voltage and currentsignals of frequency f is given by:

$\begin{matrix}{{\Phi (f)} = {\tan^{- 1}( \frac{\frac{1}{2\pi \; {fC}} - {2\pi \; {fL}}}{R} )}} & (2)\end{matrix}$

At the resonant frequency f₀ the impedance is at a minimum and thus:

$\begin{matrix}{{\frac{1}{2\pi \; f_{0\; C}} = {2\; \pi \; f_{0}L}};{and}} & (3) \\{{Z( f_{0} )} = {R.}} & (4)\end{matrix}$

Accordingly, the value of R may be determined empirically, for exampleby calculating, measuring or otherwise determining the impedance at theresonant frequency, Z(f₀). It should be noted however that the value ofR might also be determined by other means, for example applying a DCvoltage signal to the circuit and measuring the impedance, which may besubstantially equal to the resistance.

Further, if the value of C is known (for example by testing prior toshipping to the customer, since variations in the wire loop typicallywill not alter the capacitance of the circuit), equation 3 may berearranged to give L in terms of known values f₀ and C:

$\begin{matrix}{L = \frac{1}{( {2\pi \; f_{0}} )^{2}C}} & (5)\end{matrix}$

Such a known value for C might be stored or predefined within thecontrol system 15, for example by being stored on data storage formingpart of the control system 15, or by being predefined within theprogramming of the processor(s) 16.

Equation 5 may be substituted into equations 1 and 2 to give expressionsfor Z(f) and Φ(f) in terms of known values f₀, R and C:

${Z(f)} = \sqrt{R^{2} + ( \frac{f_{0}^{2} - f^{2}}{2\; \pi \; f_{0}^{2}f\; {RC}} )^{2}}$${\Phi (f)} = {\tan^{- 1}( \frac{f_{0}^{2} - f^{2}}{2\; \pi \; f_{0}^{2}f\; {RC}} )}$

If we know that a sinusoidal voltage waveform of frequency f results ina phase shift of Φ(f) and we are seeking a suitable phase shift Ill _(k)for the kth sinusoidal voltage waveform of the operating voltagewaveform V(t) such that the corresponding kth sinusoidal currentwaveform will have a phase shift value of θ_(k), then the phase shiftfor frequency f_(k), Φ(f_(k)), may simply be subtracted from the desiredphase shift value, θ_(k). Thus:

ψ_(k)=θ_(k)−Φ(f _(k))

Similarly, if we know that a sinusoidal voltage waveform of frequency fresults in a current amplitude that is scaled by a factor

$\frac{1}{Z(f)}$

and we are seeking a suitable voltage amplitude value A_(k) for the kthsinusoidal voltage waveform of the operating voltage waveform V(t) suchthat the corresponding kth sinusoidal current waveform will have anamplitude of B_(k), then A_(k) should be equal to B_(k) multiplied bythe impedance value Z(f_(k)) for frequency f_(k). Thus:

A _(k) =Z(f _(k))B _(k)

Accordingly, it is possible to determine suitable parameter values (e.g.phase shift and amplitude values ψ_(k), A_(k)) for the sinusoidalvoltage waveforms of the operating voltage waveform.

The operating voltage waveform V(t) may therefore be expressed as:

${V(t)} = {\sum\limits_{k = 1}^{n}{{Z( f_{k\;} )}B_{k}{\sin ( {{2\pi \; f_{k}t} + \theta_{k} - {\Phi( f_{k}\; )}} )}}}$

Or, more fully:

${V(t)} = {\sum\limits_{k = 1}^{n}{B_{k}\sqrt{R^{2} + ( \frac{f_{0}^{2} - f_{k}^{2}}{2\; \pi \; f_{0}^{2}f_{k}\; {RC}} )^{2}}{\sin ( {{2\pi \; f_{k}t} + \theta_{k} - {\tan^{- 1}( \frac{f_{0}^{2} - f_{k}^{2}}{2\; \pi \; f_{0}^{2}f_{k}\; {RC}} )}} )}}}$

It should be noted that these equations are simply one specific exampleof how to derive an algebraic expression for each of the impedance Z(f)and the phase difference Φ(f) at frequency f, in terms of the frequencyin question f, the resonant frequency f₀, and one or more known valuescorresponding to the other sources of resistance and/or capacitancewithin the same circuit as the wire loop 20 and how to determinesuitable parameter values (e.g. phase shift and amplitude values ψ_(k),A_(k)) for the sinusoidal voltage waveforms of the operating voltagewaveform using such known values and the calculated value of theresonant frequency f₀. Accordingly, it should be appreciated that anumber of other examples are possible, with the specific algebraicexpressions depending on the components and topology of the circuit thatthe wire loop 20 forms part of.

Comparison of the First and Second Example Approaches

It should be noted that the first example approach may, in some cases,require relatively more accurate timing measurements to find the phaseshift between the voltage and current. The second example approach maytherefore be somewhat simpler to implement and more robust, as itrequires only current measurements and also the peak frequency accuracyis less critical.

Activating the Calibration Mode

The processor(s) 16 may be programmed so as enter the calibration modein response to the occurrence of certain events, which are definedwithin their programming. In one example, processor(s) 16 may beprogrammed so as enter the calibration mode upon initialization of thedemarcating system, for instance every time the user turns on thedemarcating system. In another example, the processor(s) 16 may beprogrammed so as enter the calibration mode upon receipt by the systemof a user command, for instance provided using a user interface on thebase station 10, or provided wirelessly (e.g. from the user's smartphone, tablet or other computing device). In another example, theprocessor(s) 16 may be programmed so as enter the calibration modeperiodically, for instance every day (preferably at a time that the useris unlikely to be using the system).

Demarcating Mode

Once the demarcating system has been calibrated (for example accordingto one of the approaches described above) so as to determine a suitableoperating voltage waveform, the processor(s) 16 may be programmed so asto enter a demarcating mode. In such a demarcating mode, theprocessor(s) 16 may cause the signal generator 12 to apply the operatingvoltage waveform to the wire loop, which causes the emission of acorresponding electromagnetic boundary indicating signal from the wireloop for receipt by the receiver 101 of the object 50. In a particularexample, the receiver 101 of the receiving system 100 may, be configuredto sense the time-varying magnetic field component of theelectromagnetic boundary indicating signals emitted by the wire loop 20.

The processor(s) 102 of the receiving system 100 may be programmed so asto determine the location of the object 50 relative to the boundaryindicated by the wire loop 20, using the received electromagneticsignals. For instance, they may be able to determine whether the object50 is inside of, or outside of the boundary indicated by the wire loop20 and/or to determine an estimate of the object's distance from thewire loop 20 (e.g. using the relative strength of the electromagneticsignal, for example, of its magnetic field component).

As noted above, where the object 50 is a robotic lawnmower, the wireloop 20 may, for example, indicate to the robot the path of at leastpart of a boundary of an area to be mowed (e.g. at least a part of theedge of a lawn). In such a case the processor(s) 102 of the receivingsystem 100 may be programmed so as to determine the location of therobot 50 relative to the boundary of the area to be mowed, using theelectromagnetic signals received from the wire loop 20.

Further Modifications and Variations

It should be understood that the examples of demarcating systems androbotic systems presented above are merely illustrative and that a widevariety of variations and modifications of such examples are possiblewithout departing from the principles of the present invention.

1. A demarcating system for indicating a boundary of an area to anobject, the object having a receiver for receiving electromagneticsignals, the system comprising: a control system comprising one or moreprocessors; a wire loop, which may be arranged by a user along a path,so that said path is indicated to the object as at least part of theboundary of the area, a length of the wire loop being adjustable by theuser; a signal generator, which is electrically connected to the wireloop so as to be operable to apply voltage signals thereto, which causethe emission of corresponding electromagnetic boundary indicatingsignals from the wire loop for receipt by the receiver of the object,the signal generator being under the control of the control system suchthat the voltage signals applied by the signal generator to the wireloop are controlled by the control system; current sensing circuitry,which is electrically connected to the wire loop so as to sense currentsignals present within the wire loop and which is connected to thecontrol system so that its processors can analyse current signalspresent within the wire loop; wherein the one or more processors areprogrammed to operate in a calibration mode whereby they: cause thesignal generator to apply a series of test voltage waveforms to the wireloop, each of the test voltage waveforms generating a correspondingcurrent waveform within the wire loop; and analyse the series ofcorresponding current waveforms, as sensed by the current sensingcircuitry, so as to determine an operating voltage waveform that, whenapplied to the wire loop, generates a corresponding operating currentwaveform that, when normalized, is substantially the same as apredetermined current waveform.
 2. A demarcating system according toclaim 1, wherein the operating current waveform is substantially thesame as the predetermined current waveform.
 3. A demarcating systemaccording to claim 1, wherein each of the series of test voltagewaveforms is substantially sinusoidal and has a respective frequency. 4.A demarcating system according to claim 1, wherein the predeterminedcurrent waveform is bipolar and polarity asymmetric.
 5. A demarcatingsystem according to claim 1, wherein a complete cycle of thepredetermined current waveform comprises a number of positive peaks anda number of negative peaks, said number of positive peaks beingdifferent than said number of negative peaks.
 6. A demarcating systemaccording to claim 1, wherein the predetermined current waveform may berepresented as a superposition of sinusoidal current waveforms, eachhaving a respective frequency f_(k), phase shift 0 _(k), and amplitudevalue B_(k); and wherein the operating voltage waveform may berepresented as a superposition of n sinusoidal voltage waveforms, eachhaving a respective phase shift ψ_(k), and amplitude value A_(k) andhaving the same frequency f_(k) as a respective one of the n sinusoidalcurrent waveforms; and wherein n is less than or equal to 10 .
 7. Ademarcating system according to claim 1, wherein the predeterminedcurrent waveform may be represented as a superposition of n sinusoidalcurrent waveforms, each having a respective frequency f_(k) and phaseshift θ_(k); and wherein the series of test voltage waveforms comprisessinusoidal test voltage waveforms, each with the same frequency, f_(k),as a respective one of the n sinusoidal current waveforms.
 8. Ademarcating system according to claim 7, wherein the one or moreprocessors are programmed such that analysing the series ofcorresponding current waveforms includes determining the phasedifference between each test voltage waveform and its correspondingcurrent waveform, thereby providing a corresponding series of phasedifference values, Φ₁. . . Φ_(m).
 9. A demarcating system according toclaim 8, wherein said operating voltage waveform may be represented as asuperposition of n sinusoidal voltage waveforms; and wherein each of then sinusoidal voltage waveforms of the operating voltage waveform has thesame frequency, f_(k), as a corresponding one of the n sinusoidalcurrent waveforms of the predetermined current waveform, and has a phaseshift that is a combination of the phase shift, θ_(j), of that one ofthe n sinusoidal current waveforms, less the phase difference value,Φ_(k), associated with the test voltage waveform having the samefrequency f_(k).
 10. A demarcating system according to claim 8, whereinthe one or more processors are programmed such that analysing the seriesof corresponding current waveforms includes determining, for each testvoltage waveform v_(k)(t), the ratio between its amplitude a_(k) andthat of its corresponding current waveform i_(k)(t), thereby providing acorresponding series of impedance values Z_(k).
 11. A demarcating systemaccording to claim 10, wherein each of the n sinusoidal currentwaveforms of the predetermined current waveform I(t) has a respectiveamplitude value, B,_(k); and wherein each of the n sinusoidal voltagewaveforms of the operating voltage waveform has a frequency f_(k) and anamplitude that is substantially proportional to, and substantially equalto, the product of: the impedance value, Z_(k), associated with the testvoltage waveform f_(k)(t). having the same frequency, f_(k); and theamplitude value, B_(k), for the sinusoidal current waveform having thesame frequency.
 12. A demarcating system according to claim 1, whereineach of the series of test voltage waveforms has substantially a sameshape, but a different respective frequency, the frequencies of theseries of test voltage waveforms being distributed over a frequencyrange; wherein the one or more processors are programmed such thatanalysing the series of corresponding current waveforms includesdetermining a resonant frequency, f₀ within said frequency range;wherein said resonant frequency is such that a voltage waveform ofsubstantially the same shape as said test waveforms and having saidresonant frequency will generate a corresponding current waveform havinga maximum amplitude as compared with current waveforms that aregenerated by voltage waveforms of the same shape as said test waveformsand have other frequencies within said frequency range.
 13. Ademarcating system according to claim 12, wherein the one or moreprocessors are programmed such that analysing the series ofcorresponding current waveforms further includes determining animpedance at the resonant frequency, f₀.
 14. A demarcating systemaccording to claim 1, wherein each of the series of test voltagewaveforms is substantially sinusoidal and has a respective frequency,the frequencies of the series of test voltage waveforms beingdistributed over a frequency range; and wherein the one or moreprocessors are programmed such that analysing the series ofcorresponding current waveforms includes determining the a resonantfrequency, f₀ within said frequency range, a sinusoidal voltage waveformhaving said resonant frequency generating a corresponding currentwaveform having the maximum amplitude as compared with current waveformsgenerated by sinusoidal voltage waveforms with other frequencies withinsaid frequency range.
 15. A demarcating system according to claim 14,wherein the one or more processors are programmed such that analysingthe series of corresponding current waveforms further includesdetermining an impedance at the resonant frequency, f₀.
 16. Ademarcating system according to claim 15, wherein the predeterminedcurrent waveform may be represented as a superposition of n sinusoidalcurrent waveforms, each having a respective frequency f_(k) and phaseshift θ_(k); and wherein the operating voltage waveform may berepresented as a superposition of sinusoidal voltage waveforms; andwherein each of the sinusoidal voltage waveforms has the same frequency,f_(k), as a corresponding one of the plurality of sinusoidal currentwaveforms and has a phase shift that is a combination of the phase shiftof that sinusoidal current waveform, θ_(k), and an additional phaseshift value, Φ_(k), which is determined by said one or more processorsbased on: the frequency of that sinusoidal current waveform, f_(k); theresonant frequency, f₀, and one or more values corresponding to theother sources of resistance and/or capacitance within the same circuitas the wire loop.
 17. A demarcating system according to claim 16,wherein each impedance value, Z(f_(k)), as determined by said one ormore processors, is additionally based on said impedance, Z(f₀), at theresonant frequency, f₀.
 18. A demarcating system according to claim 16,wherein all of the sources of resistance within the same circuit as thewire loop may be approximated as a single source of resistance having aresistance R; wherein all of the sources of capacitance within the samecircuit as the wire loop may be approximated as a single source ofcapacitance in series with the wire loop and having a capacitance C; andwherein each of said additional phase shift values is substantiallyequal to:$\tan^{- 1}( \frac{f_{0}^{2} - f^{2}}{2\; \pi \; f_{0}^{2}f\; {RC}} )$19. A demarcating system according to claim 18, wherein the one or moreprocessors are programmed such that analysing the series ofcorresponding current waveforms further includes determining theimpedance, Z(f₀), at the resonant frequency, f₀; and wherein saidresistance H is taken as being equal to said impedance, Z(f₀), at theresonant frequency, f₀.
 20. A demarcating system according to claim 18,wherein said capacitance C is a predefined value stored by the controlsystem.
 21. A demarcating system according to claim 16, wherein each ofthe plurality of sinusoidal current waveforms of the predeterminedcurrent waveform has a respective amplitude value B_(k); and whereineach of the sinusoidal voltage waveforms of the operating voltagewaveform has an amplitude that is substantially proportional to, andsubstantially equal to, the product of: an impedance value, Z_(k),calculated for a sinusoidal voltage waveform having the same frequency,f_(k); and the amplitude value, B_(k), for the sinusoidal currentwaveform having the same frequency, f_(k); and wherein each impedancevalue Z (f_(k)) is determined by said one or more processors based on:the frequency, f_(k), of the sinusoidal voltage waveform in question;the resonant frequency, f₀; and one or more values corresponding to theother sources of resistance and/or capacitance within the same circuitas the wire loop.
 22. A demarcating system according to claim 21,wherein each impedance value, Z(f_(k)), as determined by said one ormore processors, is additionally based on said impedance, Z(f₀), at theresonant frequency, f₀.
 23. A demarcating system according to claim 21,wherein all of the sources of resistance within the same circuit as thewire loop may be approximated as a single source of resistance having aresistance R; wherein all of the sources of capacitance within the samecircuit as the wire loop may be approximated as a single source ofcapacitance in series with the wire loop and having a capacitance C; andwherein each impedance value z(f_(k)) is substantially equal to:$\sqrt{R^{2} + ( \frac{f_{0}^{2} - f_{k}^{2}}{2\; \pi \; f_{0}^{2}f_{k}\; C} )^{2}}$24. A demarcating system according to claim 23, wherein the one or moreprocessors are programmed such that analysing the series ofcorresponding current waveforms further includes determining theimpedance, Z(f₀), at the resonant frequency, f₀; and wherein saidresistance R is taken as being equal to said impedance, Z(f₀), at theresonant frequency, f₀.
 25. A demarcating system according to claim 23,wherein said capacitance C is a predefined value stored by the controlsystem.
 26. A demarcating system according to claim 1, wherein theobject is a robot.
 27. A demarcating system according to claim 26,wherein the object is a robotic lawnmower.
 28. A demarcating systemaccording to claim 27, wherein the wire loop indicates to the robot thepath of at least part of a boundary of an area to be mowed.
 29. Ademarcating system according to claim 1, wherein the one or moreprocessors are programmed to enter said calibration mode: uponinitialization of the demarcating system; upon receipt by the system ofa user command; and/or periodically.
 30. A demarcating system accordingto claim 1, wherein the one or more processors are programmed to operatein a demarcating mode whereby they: cause the signal generator to applysaid operating voltage waveform to the wire loop, which causes theemission of a corresponding electromagnetic boundary indicating signalfrom the wire loop for receipt by the receiver of the object.
 31. Arobotic system comprising the demarcating system according to claim 1and a robot, the robot comprising: a receiver for receivingelectromagnetic signals from the demarcating system; and one or moreprocessors programmed to determine the location of the robot relative tothe boundary indicated by the wire loop, using said receivedelectromagnetic signals.
 32. A module for the demarcating system ofclaim 1, the module comprising said control system, said signalgenerator and said current sensing circuitry and being connectable tosaid wire loop; optionally wherein the module is configured as acharging station for the object.